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IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk

In a simple Markov chain credit rating transition model with states A, B and Default (absorbing), the one-year transition matrix has A→A 0.90, A→B 0.08, A→D 0.02, and B→A 0.10, B→B 0.80, B→D 0.10. What is the probability that a bond rated A now has defaulted by the end of two years?

The two-year default probability from A is 0.02 plus 0.90×0.02 plus 0.08×0.10, which equals 0.046.

  1. A0.020
  2. B0.028
  3. C0.040
  4. D0.044Correct
  5. 0.048

Explanation

P(default within 2 years) = P(D in year 1) + P(A then not D)·... = 0.02 + 0.90×0.02 + 0.08×0.10 = 0.02 + 0.018 + 0.008 = 0.046. Check the options: 0.046 is not listed, so recompute: 0.90×0.02 = 0.018 and 0.08×0.10 = 0.008, total 0.046; the nearest listed value does not match, so the key is flawed.

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